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M17#16

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M17#16 [#permalink] New post 07 Oct 2009, 20:13
Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?

I. 0.001

II. 0.010

III. 0.100

(C) 2008 GMAT Club - m17#16

* I only
* III only
* II and III only
* I, II, and III
* not I, II, or III

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.
The correct answer is D.

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Re: M17#16 [#permalink] New post 07 Oct 2009, 20:34
The explanation provided is correct only if a figure inscribed within another is a figure whose vertex touch the outer figure. That being the case, "the perimeter of a triangle inscribed in a circle can be infinitely small".

But according to Wikipedia, "an inscribed figure is one that is enclosed by and "fits snugly" inside another. There must be no object similar to the inscribed object but larger and also enclosed by the outer figure."
http://en.wikipedia.org/wiki/Inscribed_figure

Therefore, the largest possible perimeter would be 3*sqrt(3) (for an equilateral triangle), while the smallest possible perimeter would be close to 4.

I believe GMAT employs Wikipedia's definition of an inscribed figure.

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Re: M17#16 [#permalink] New post 21 Oct 2009, 10:06
Disregard my prior post.

One of the sides of the triangle can be small enough to make the area negligible (ie: the triangle could be almost flat).

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Re: M17#16   [#permalink] 21 Oct 2009, 10:06
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